Contour integration for the view factor calculation between two rectangular surfaces

The calculation of the view factor is an important consideration in radiative heat transfer analysis. Thermal engineering requires the view factor calculations between complex geometries containing parallel and inclined surfaces. There is currently no analytic formula available for this, so the summation rule (SR) must be used. However, when complex geometries are analyzed, processing SR becomes a very intensive task. Therefore, the present study aims to exploit vector calculus to develop a formula for calculating the view factors for radiative heat transfer from any two rectangular oblique or parallel surfaces. The exact solution obtained by means of the contour integration was compared with the numerical integration of the quadruple integral using the multiple Simpson's rule 1/3 with five intervals (MSR) and the summation rule via the Hamilton-Morgan solution (HMS). The lack of similar precedents in the literature reinforces the scientific and practical nature of the proposed method.